Online and semi-online scheduling on two hierarchical machines with a common due date to maximize the total early work

In this study, we investigated several online and semi-online scheduling problems on two hierarchical machines with a common due date to maximize the total early work. For the pure online case, we designed an optimal online algorithm with a competitive ratio of $\sqrt 2$. For the case when the total processing time is known, we proposed an optimal semi-online algorithm with a competitive ratio of $\frac{4}{3}$. Additionally, for the cases when the largest processing time is known, we gave optimal algorithms with a competitive ratio of $\frac{6}{5}$ if the largest job is a lower hierarchy one, and of $\sqrt 5-1$ if the largest job is a higher hierarchy one, respectively

A survey of scheduling problems with late work criteria

The paper presents the first complete survey of scheduling problems with the late work criteria. Late work objective functions estimate the quality of a schedule based on durations of late parts of jobs, not taking into account the amount of delay for fully late jobs. The paper provides a formal definition of the late work parameter and compares the criteria based on it with other classical performance measures. It shows the relationship between the late work model and the imprecise computation model known from the hard real-time literature. Moreover, the paper presents a few real world applications of the late work objective function. The paper lists results obtained for nearly forty problems of scheduling jobs on a single machine, parallel (identical and uniform) machines and dedicated machines, investigated in the literature since 1984.Scheduling Late work Single machine Parallel machines Dedicated machines

A novel representation of graph structures in web mining and data analysis

The paper presents a new graph representation, the graph matrix, which combines the adjacency matrix with the linked lists allowing for the fastest possible access to different types of information on a graph. This is increasingly important for a high search performance, for instance, for rapidly extracting information from the link structure in a hub and authority graph of the World-Wide-Web. A very recent application for the proposed data structure arises from categorical data clustering defining proximity and similarity of data through their patterns of co-occurrence.Graph representation Data structure Data analysis

Complexity of Scheduling Problem in Single-Machine Flexible Manufacturing System with Cyclic Transportation and Unlimited Buffers

International audienc

Exact Approaches to Late Work Scheduling on Unrelated Machines

We consider the scheduling problem on unrelated parallel machines in order to minimize the total late work. Since the problem is NP-hard, we propose a mathematical model and two dedicated exact approaches for solving it, based on the branching and bounding strategy and on enumerating combined with a dynamic programming algorithm. The time efficiencies of all three approaches are evaluated through computational experiments

Exact approaches to late work scheduling on unrelated machines

We consider the scheduling problem on unrelated parallel machines in order to minimize the total late work. Since the problem is NP-hard, we propose a mathematical model and two dedicated exact approaches for solving it, based on the branching and bounding strategy and on enumerating combined with a dynamic programming algorithm. The time efficiencies of all three approaches are evaluated through computational experiments